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Questions › Mathematics › Coordinate and solid geometry

Coordinate and solid geometry: previous year questions

Asked 18 times in 2 exams across 9 years. Newest first.

Practise Coordinate and solid geometry, easy to hard →

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  • Coordinate geometry: distance, lines and circles 6
  • Solid geometry: the cube and three dimensions 7
  • Areas, polygons and the Pythagorean theorem 5

Coordinate geometry: distance, lines and circles

Using coordinates to find distances, slopes and the equation of a circle.

  1. JNU 2020 Q29If equation of lines 4x–ky=6 and 6x+3y+2=0 are perpendicular then,
  2. DSE 2019 Q10The line y=2x+5 is tangent to a circle with equation x²+y²+16x+12y+c=0, at point P. So, P equals
  3. JNU 2017 Q19In the standard (x, y) coordinate plane, the graph of (x + 3)² + (y + 5)² = 16 is a circle. What is the circumference of the circle, expressed in…
  4. JNU 2017 Q38Line L₁ passes through the points (-2, 0) and (0, k). Line L₂ passes through the points (4, 0) and (6, 2). What value of k makes the two lines…
  5. DSE 2014 Q5Let O(0,0), P(3,4) and Q(6,0) be the vertices of triangle OPQ. If a point S in the interior is such that triangles OPS, PQS and OQS have equal area…
  6. JNU 2011 Q4A line that is 13 units long has (4, 1) as one of the endpoints. Which of the following could be the other endpoint?

Solid geometry: the cube and three dimensions

Vertices, surfaces and volume of solids in three dimensions.

  1. DSE 2014 Q18Suppose a straight line in ℝ³ passes through the point (-1,3,3) in the direction of the vector (1,2,3). The line will hit the xy -plane at the point
  2. JNU 2013 Q44The intersection of three distinct planes in the three-dimensional space is
  3. JNU 2012 Q7Which of the following is true?
  4. JNU 2012 Q8Which of the following is true?
  5. JNU 2012 Q9Which of the following is true?
  6. JNU 2012 Q10Which of the following is true?
  7. DSE 2008 Q20Suppose we have a chair with n legs and it stands with all its legs touching the floor, regardless of the floor quality, i.e., evenness, smoothness…

Areas, polygons and the Pythagorean theorem

Areas of plane figures and right-angle distances.

  1. DSE 2021 Q12Consider a triangle with sides AC = 2, AB = √3 and BC = 1. Choose a random point P inside the triangle. The minimum distances from P to AC, AB and…
  2. JNU 2012 Q6If three corners of a parallelogram are (1, 1), (4, 2) and (1, 3), then the fourth corner is
  3. JNU 2012 Q54Two men, starting at the same point, walk in opposite directions for 4 meters, turn left and walk another 3 meters. What is the distance between them?
  4. JNU 2011 Q2If the radius of a circle is increased by 20%, then the area is increased by
  5. JNU 2011 Q81A circle of area A passes through the points (8, 0) and (0, 6). Then we must have